{"id":"W2009089486","doi":"10.1007/s00222-014-0508-1","title":"Diophantine equations in the primes","year":2014,"lang":"en","type":"article","venue":"Inventiones mathematicae","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":31,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; Diophantine equation; Integer (computer science); Type (biology); Prime (order theory); Degree (music); Combinatorics; Prime number; Discrete mathematics","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003427805,0.0001347183,0.0002449731,0.0001424432,0.0001282335,0.00007263863,0.0004965579,0.00005323506,0.0006670655],"category_scores_gemma":[0.003415026,0.00008820653,0.0001219476,0.0004341507,0.0001301195,0.0001178436,0.00007638738,0.0001803625,0.0005785439],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002451194,"about_ca_system_score_gemma":0.00002324803,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000007187345,"about_ca_topic_score_gemma":0.00002660557,"domain_scores_codex":[0.9981276,0.0004179229,0.0004722822,0.0001855838,0.0005121432,0.0002844932],"domain_scores_gemma":[0.996452,0.00266585,0.0001300208,0.000636949,0.00007005908,0.00004510616],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.000003618708,0.0002871382,0.0002187639,0.0001463265,0.0000181892,0.000002237684,0.001051783,0.00000161551,0.00008376556,0.996458,0.001165355,0.0005631856],"study_design_scores_gemma":[0.0003097793,0.00002428538,0.0003316706,0.0001046622,0.00003139931,0.00001428968,0.000549537,0.006491441,0.0001599374,0.9910649,0.0008117171,0.0001063604],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5054449,0.0000725272,0.3462263,0.006359436,0.0001482093,0.001413486,0.000004802052,0.000243476,0.1400869],"genre_scores_gemma":[0.9893613,0.0000025998,0.007243702,0.0001227045,0.00009425773,0.0001131946,0.000004192569,0.00002499984,0.003033064],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4839164,"threshold_uncertainty_score":0.7436205,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.09882583270690458,"score_gpt":0.3761525573862886,"score_spread":0.277326724679384,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}